If log[x+y/3]=1/2[logx+logy]=1/2[logx+logy] find the value of x/y+y/x
Answers
Answered by
105
Question:
if
find the value of
Solution :
use property :
log(a) + log (b) = log (ab)
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use property log (a/b) = log a- log b
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use property :
Now use property ;
log (x/y ) = logx -logy
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it is the required solution!
Properties of logarithm :
Answered by
15
log(x+y/3) = 1/2(log x + log y)
log(x+y/3) = 1/2 log (xy)
log(x+y/3) = log (xy)1/2
log(x+y/3) = log (√xy)
REMOVE LOG ON BOTH SIDES
(x+y/3) = √xy
SQUARING ON BOTH SIDES
(x+y/3)² = (√xy)²
(x+y)²/(3)² = xy
(x+y)²/9 = xy
(x+y)² = 9xy
x²+y²+2xy = 9xy
x²+y² = 9xy-2xy
x²+y² = 7xy
x²+y²/xy = 7
x²/xy + y²/xy = 7
x/y + y/x = 7
HOPE THIS HELPS U MATE...
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